Last week, Mayor de Blasio told state lawmakers that they’d be foolish to confuse two separate issues. The first is approving an income-tax hike on Gotham’s wealthy to bring in half a billion dollars a year for new funding for pre-K and after-school programs. The second is the city’s long-expired union contracts. “There is no connection whatsoever,” de Blasio promised. Well . . . only if you’re disconnected from fiscal reality.

What makes up nearly all of the cost of preschool? Pay — and retirement and health benefits — for union members.

And how do we know how much that pay and benefits will cost? We don’t — until we have union contracts.

Bad union deals could increase the pre-K cost by tens of millions of dollars a year.

It’s easy to see where pre-K dollars will go. Look at where current pre-K spending goes. This year, the city will spend $191.6 million in pre-K classrooms. (It will spend another $40 million or so busing kids to and from pre-K and keeping the lights and heat on.)

Of that $191.6 million, 97 percent is for teacher pay or benefits.

Now, to serve 55,000 kids at least for a half a day, the city already has 1,202 pre-K teachers, who make an average of $105,400, once you include the city’s pension contribution and health benefits.

Each class needs a teacher aide, too — another 1,202 people, who make an average $48,800 with benefits.

To serve 73,250 full-day students in 18 months’ time, de Blasio needs to hire “around 2,000” new “lead teachers,” he says — and, presumably, an equal number of classroom aides. That’s $308.5 million new spending just on teacher pay and salaries — a little less than the $340 million he wants from his tax hike (the balance of the $500 million would go to after-school programs).

Now, those current pre-K teachers and aides have been working without a contract for nearly half a decade — which is why it’s bizarre to say, as de Blasio said last week, that pre-K and labor issues are “two ships passing in the night.”

They’re more like two ships crashing in the night.

Consider: What if de Blasio were to award a pay raise of, say, 9 percent, to make up for inflation over five years? That would add $27.8 million a year to the cost of new pre-K spending alone.

Retroactive raises for all teachers would require $3.5 billion up front, as the Citizens’ Budget Commission has reported — or enough to pay for new preschool for 10 years.

In fact, de Blasio doesn’t have to pay preschool teachers six figures’ worth of salary and benefits. As the mayor said himself, 2,000 preschool teachers graduate each year — meaning plenty of supply to meet demand.

But there are clues that the mayor will pay well. In a white paper, he pledged that “pay levels across the system will be sufficient to attract and retain the best certified teachers.”

That document also said that the city’s Department of Education — practically speaking, the teacher’s union — will review each program for quality.

Don’t expect the union to accept new classrooms with people who may know how to supervise 4-year-olds as they draw, rhyme and sing — but who lack high-priced certification.

Whether or not you think it’s a good idea to pay teachers a lot (and give them free health benefits), it makes no fiscal sense for either the Legislature — or the City Council, which must sign off on the city budget — to agree to any funding for new preschool before we know how much it’s going to cost.

That’s especially true because, under the current interpretation of the state Constitution, once the city hires a teacher, the city can never reduce that teacher’s pension benefits or demand a higher pension contribution.

At the Albany hearing, de Blasio warned about the “profoundly great, great unknown of the open labor contracts.”

Retroactive contracts for 300,000 workers are “going to add additional fiscal stresses,” he said. “We don’t actually know which day it will be resolved,” but “this will be resolved, and there will be a cost.”

If de Blasio wants to reopen Bloomberg’s balanced budget and spring a multibillion-dollar surprise on the public, he should say so — before he gets another dollar to add one more person to the payroll.

Nicole Gelinas is a contributing editor to the Manhattan Institute’s City Journal.